$J$ is the midpoint of $\overline{CT}$ $C$ $J$ $T$ If: $ CJ = 8x + 5$ and $ JT = 9x - 4$ Find $CT$.
Solution: A midpoint divides a segment into two segments with equal lengths. ${CJ} = {JT}$ Substitute in the expressions that were given for each length: $ {8x + 5} = {9x - 4}$ Solve for $x$ $ -x = -9$ $ x = 9$ Substitute $9$ for $x$ in the expressions that were given for $CJ$ and $JT$ $ CJ = 8({9}) + 5$ $ JT = 9({9}) - 4$ $ CJ = 72 + 5$ $ JT = 81 - 4$ $ CJ = 77$ $ JT = 77$ To find the length $CT$ , add the lengths ${CJ}$ and ${JT}$ $ CT = {CJ} + {JT}$ $ CT = {77} + {77}$ $ CT = 154$